(square roots of the identity matrix) For how many

Chardonnay Felix
2021-03-08
Answered

(square roots of the identity matrix) For how many

You can still ask an expert for help

au4gsf

Answered 2021-03-09
Author has **95** answers

Step 1

To find how many matricec A of order 2 exists such that

Here we have to find

Let us consider any arbitrary matrix of order 2.

Then

Now from

Step 2

Case 1:

If

From (3) we get :

From (4) we get :

From (1) we get :

From (2) we get :

Therefore we get the matrix of the form

Step 3

Case 2:

If

sub case a:

If a=0 , that implies

Then from(1 ) and (2) , we get :

Therefore we get the matrix of the form

Step 4

We can also consider further subcases to find the type of involuntary matrices, but as the question is asked to find how many, we have already got infinitely many

Similarly for any

Jeffrey Jordon

Answered 2022-01-22
Author has **2313** answers

Answer is given below (on video)

Jeffrey Jordon

Answered 2022-01-30
Author has **2313** answers

Answer is given below (on video)

asked 2021-01-31

Find a basis for the space of $2\times 2$ diagonal matrices.

$\text{Basis}=\{\left[\begin{array}{cc}& \\ & \end{array}\right],\left[\begin{array}{cc}& \\ & \end{array}\right]\}$

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Let B be a 4x4 matrix to which we apply the following operations:

1. double column 1,

2. halve row 3,

3. add row 3 to row 1,

4. interchange columns 1 and 4,

5. subtract row 2 from each of the other rows,

6. replace column 4 by column 3,

7. delete column 1 (column dimension is reduced by 1).

(a) Write the result as a product of eight matrices.

(b) Write it again as a product of ABC (same B) of three matrices.

1. double column 1,

2. halve row 3,

3. add row 3 to row 1,

4. interchange columns 1 and 4,

5. subtract row 2 from each of the other rows,

6. replace column 4 by column 3,

7. delete column 1 (column dimension is reduced by 1).

(a) Write the result as a product of eight matrices.

(b) Write it again as a product of ABC (same B) of three matrices.

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When does ${\mathrm{arcsin}}^{2}x+{\mathrm{arccos}}^{2}x=1$ for x real or comlex?

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Can someone prove that $\sum _{i=1}^{89}{\mathrm{sin}}^{2n}\left(\frac{\pi}{180}i\right)$ is a dyadic rational for all positive integers n, or find counterexample?

asked 2021-11-22

a) By inspection, find a particular solution of

$y+2y=10$

b) By inspection, find a particular solution of

$y+2y=-4x$

c) Find a particular solution of

$y+2y=-4x+10$

d) Find a particular solution of

$y+2y=8x+5$

b) By inspection, find a particular solution of

c) Find a particular solution of

d) Find a particular solution of

asked 2022-07-18

For a real vector I know we write $a=({a}_{1},{a}_{2},{a}_{3})\in {\mathbb{R}}^{3}$, which means ${a}_{1}\in \mathbb{R}$, ${a}_{2}\in \mathbb{R}$ and ${a}_{3}\in \mathbb{R}$

Suppose instead I have a vector $b=({b}_{1},{b}_{2},{b}_{3})$ where ${b}_{1}$, ${b}_{2}$ and ${b}_{3}$ only takes the values 0 or 1. What is the correct notation for this?

Suppose instead I have a vector $b=({b}_{1},{b}_{2},{b}_{3})$ where ${b}_{1}$, ${b}_{2}$ and ${b}_{3}$ only takes the values 0 or 1. What is the correct notation for this?

asked 2022-01-17

My work with complex numbers verified that the only possible cube root of 8 is 2. Determine whether the statement makes sense or does not make sense, and explain your reasoning.